Changes to contacts not saving when "Use another contact's address" is checked

Contacts that have the option "Use another contact's address" option checked can no longer be edited using the full edit screen.

Steps to reproduce:
Create a Household, enter a name and an address.
Create an Individual, enter a name, go to the address section and check "Use another contact's address" and select the Household you just created. Save this contact. You are now returned to the 'View Contact' screen.
Click 'Edit' and try to change something about this contact, such as entering an E-mailaddres, phone number or External ID. Click 'Save'. CiviCRM reports that the contact has been updated, but no changes are visible in the 'View Contact' screen.

Workarounds:
1) 'Ajax-option': For those fields where in-place editing is possible on the 'View Contact' screen, one can use this option to make changes that will be saved. This however doesn't work for fields like 'External ID' (which we use to link contacts to barcodes on membership cards) or contact photo, which don't offer in-place editing.
2) Edit the contact, take note of the household used for the address, uncheck the "Use another contact's address" option, Save the contact, Edit again, making the necessary changes, Save. Edit again, check "Use another contact's addres" and reselect the household that you noted earlier, Save the contact again.

Issue verified in both Joomla and Drupal options on https://civicrm.org/demo